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Unformatted text preview: Economics 140A Spring 2011 Professor Startz Midterm Name: Student number: . Answer all 5 questions. Each question is worth 15 points, although some questions are easier than others. Be sure to show your work for each question. Please write your answers on the exam in the space provided after each question. Please clearly label the part of the question you are answering. Notice that there is some reference material provided after the questions. And some scrap paper too. You may use a calculator, but no other electronic devices. (No phones or laptops for example.) The exam is closed book. You may be asked to show your student id. page 2 1. Consider the usual regression estimator ̂ ¡ ¢£¤¥¢¤ ¦ . In data set 1, we get an estimate ̂ § . Now suppose you are given a new data set, data set 2, which is identical to the first set of data except that every value of ¤ has doubled. (You may assume that all our usual assumptions about the data generating process hold.) a. (3 points) Prove that if you rerun the regression for the second data set, getting ̂ ¦ , that ̂ ¦ ¡ § ¦ ̂ § . b. (4 points) Prove that ¨©ª ̂ ¦ ¡ § « ¨©ª ̂ § . c. (4 points) Prove that the reported standard error of ̂ ¦ equals § ¦ the reported standard error of ̂ § . (Remember that the reported standard error depends on ¬ ¦ rather than ¦ .) d. (4 points) Compare the t statistic on the hypothesis ¡ ® from the two regressions. page 3 2. For the sample mean, ̂ ¡ ¢ of a set of data £ ¤ £ ¡ ¥ £ ¦ , with mean zero, variance § ¨ © , and ª independent observations we know that «¬( ̂ ¡ ) ¤ ® ¯ ° ¦ . Suppose some idiot copies and pastes each observation, so the data you get handed has ±ª observations £ ¡ ¢ £ ¡ ¢ £ © ¢ £ © ¢ ¥ £ ¦ ¢ £ ¦ and you compute the sample mean, ̂ © . (Hint: It may help to write £ ² ¤ ³ ´ ² .) a. (5 points) Show that the sample mean is identical in both data sets ( ̂ ¡ ¤ ̂ © ) . (Easy.) b. (5 points) Explain intuitively why the variance of both estimators is the same. (Think for a second—very easy.) c. (5 points) Formally derive the variance of the second sample mean, without directly using the result in (b). (You may assume that the sample mean is unbiased without proving it.) (Not quite so easy.) page 4 3. This problem considers a dataset of historical gold prices for the years 17922008. The variable gold contains the price of gold in each year. The EViews output for the regression of the price of gold on the price of gold in the previous year is given below. ¡¢£ ¤ ¥ ¦ § ¨ ¦ © ¡¢£ ¤ª© ¨ « ¤ a. (10 points) Test the hypothesis that the price gold in the current year depends on the price of gold in the previous year. Be explicit about how you set up the null and alternative. Do the test at both the 5% and 1% level....
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 Fall '08
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 Economics, lower limit, dependent var, Akaike info criterion, S.D. dependent var, Statistical Tables

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